A Green’s integral representation for the two-dimensional steady Navier-Stokes equation

Chadwick, Edmund

Abstract

Consider steady uniform flow past a fixed, closed body in an unbounded domain governed
by the incompressible Navier-Stokes equations. A velocity representation is given as an integral
distribution of Green’s functions of the Navier-Stokes equations which we call NSlets, such that
the strength of the NSlets is the same as the force distribution over the body boundary. We
apply this theory to the benchmark problem of a two-dimensional circular cylinder over a range
of Reynolds numbers up to 40 when the steady flow breaks down. A boundary element code
is developed with collocation point weighting function and linear shape function, and with
Dirichlet body boundary condition that the velocity is zero. Comparison against experiment
and other numerical methods is given.

• Presentation Conference Type: Conference Paper (published)
• Start Date: Jul 8, 2019
• End Date: Jul 9, 2019
• Online Publication Date: Jul 1, 2019
• Publication Date: Jul 1, 2019
• Deposit Date: Jul 3, 2023
• Publicly Available Date: Jul 5, 2023
• Publisher: Oxford Brookes University
• Book Title: Proceedings of the 12th UK Conference on Boundary Integral Methods UKBIM12
• ISBN: 9781999741297
• Publisher URL: https://radar.brookes.ac.uk/radar/items/dd58e98a-6942-456f-98a5-0203f2a159e0/1/